Algebraic and Arithmetic Geometry Seminar

From Riemann surfaces to tropical curves (and back again)

by Martin Ulirsch (Goethe University Frankfurt am Main)

Aula Riunioni (Dipartimento di Matematica)

Aula Riunioni

Dipartimento di Matematica


The surprisingly deep analogy between compact Riemann surfaces and compact metric graphs lies at the heart of many recent developments in tropical geometry. In this talk I will give a short introduction to tropical geometry via this analogy focusing on linear systems. I will explain the process of tropicalization and discuss the realizability problem as well as some its partial solutions (and why a general solution is provably out or reach). This talk is based on joint work with Madeline Brandt, Martin Moeller and Annette Werner, as well as Dmitry Zakharov.